Answer:
A
Step-by-step explanation:
The projection of vector B on unit vector a is
(B•a)a
av(unit vector of v)= 1/√2(-1,1)
u•av= 1/√2 × (-5+7)= √2
(u•av)av= √2 × 1/√2(-1,1)= (-1,1)
First, divide the shape into two figures ( a semicircle and a rectangle)
Then, find the are or the two shapes using the area formula for a semicircle (

) and the are formula for a rectangle (base x height)
Finally, add the two areas together and you have your answer
The answer is 12.
Steps
If that number is x
(3+x)/(8+x)=3/4
"Cross multply"
4(3+x)=3(8+x)
12+4x=24+3x
x=12
To check: add 12 to 3 and 8. 3+12=15 and 8+12=20. 15/20=3/4
Answer:
Letter B matches the probability.
Step-by-step explanation:
Lucy throws a fair six sided dice.
Probability of the dice landing on a number between 1 and 6 = 
= 
On a number line fraction
can be represented by,
An small section (A to B) will represent the fraction = 
Therefore, letter B will match the probability of a dice landing on a number between 1 and 6.
Answer:
The mathematical expectation of a student who purchases 10 tickets is -$39.65.
Step-by-step explanation:
A student that purchases 10 tickets out of 2900 has a probability of winning the cruise that can be calculated as:

Each ticket cost $5, so he has spent $50 for the 10 tickets.
Then, the expected value of this operation is equal to the expected value of the earnings (probability of winning the prize multiplied by the value of the prize), minus the costs:

The mathematical expectation of a student who purchases 10 tickets is -$39.65.